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The idea of random matrix theory is applicable not only to the level statistics but also to various physical observables. Taking the dynamical conductivity in isolated quantum dots with diffusivedynamics, we investigate analytically intertwining effects of the time-reversal invariance, level repulsionand quantum interference. We clarify an ambivalent role of the time-reversal invariance at finite frequency by a new invariant analysis respecting the symmetry of the effective field theory. A subtlety of the operator insertion, and the fast-slow mode separation within the effective field description is pointed out

Universal and Nonuniversal Dynamical Conductivity in Small Metallic Grains: An Ambivalent Role of T-Invariance at Finite Frequency